Try out the lottery that is played in a far-away land. What is the chance of winning?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

In this matching game, you have to decide how long different events take.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Can you use this information to work out Charlie's house number?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

The pages of my calendar have got mixed up. Can you sort them out?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

How many trapeziums, of various sizes, are hidden in this picture?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you find all the different triangles on these peg boards, and find their angles?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.